Temporal motivation theory

Template:Multiple issues An Equated Monthly Installment (EMI) is defined by Investopedia as "A fixed payment amount made by a borrower to a lender at a specified date each calendar month. Equated monthly installments are used to pay off both interest and principal each month, so that over a specified number of years, the loan is paid off in full."

It further explains that, with most common types of loans, such as real estate mortgages, the borrower makes fixed periodic payments to the lender over the course of several years with the goal of retiring the loan. EMIs differ from variable payment plans, in which the borrower is able to pay higher payment amounts at his or her discretion. In EMI plans, borrowers are usually only allowed one fixed payment amount each month.

The benefit of an EMI for borrowers is that they know precisely how much money they will need to pay toward their loan each month, making the personal budgeting process easier.

The formula for EMI is:

$P\,=\,A\cdot {\frac {1-\left({1+r}\right)^{-n}}{r}}$

or, equivalently,

$A\,=\,P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}}$

where: P is the principal amount borrowed, A is the periodic amortization payment, r is the periodic interest rate divided by 100 (annual interest rate also divided by 12 in case of monthly installments), and n is the total number of payments (for a 30-year loan with monthly payments n = 30 × 12 = 360).

For example, if you borrow Indian Rupee 10,00,000 from the bank at 10.5% annual interest for a period of 10 years (i.e., 120 months), then EMI = Indian Rupee 10,00,000 * 0.00875 * (1 + 0.00875)120 / ((1 + 0.00875)120 – 1) = Indian Rupee 13,493. i.e., you will have to pay Indian Rupee 13,493 for 120 months to repay the entire loan amount. The total amount payable will be Indian Rupee 13,493 * 120 = Indian Rupee 16,19,220 that includes Indian Rupee 6,19,220 as interest toward the loan.